M333L - BIBLIOGRAPHY FOR TOPICS – SPRING 2003 · M333L - BIBLIOGRAPHY FOR TOPICS – SPRING 2003 Abstract symmetry in mathematics and physics • Bunch, Bryan, Reality's Mirror

M333L - BIBLIOGRAPHY FOR TOPICS – SPRING 2003

Abstract symmetry in mathematics and physics

• Bunch, Bryan, Reality's Mirror QC 174.17 S9 86 PMA

• Guillen, Michael, Bridges to Infinity,1983, pp.73-80

• Hauptmann, Herbert A., "The Role of Symmetry in Mathematical Discovery",

Symmetry v.1, 1990 27-28

• Polya, How to Solve It

• Rosen, Joe, "Symmetry, Analogy, Science", Symmetry, v.1, 1990

• Zee, A., Fearful Symmetry

Applications of geometric transformations in computer graphics

• Smart, Modern Geometry

The arbelos• Bankoff, Leon, "Are the twin circles of Archimedes really twins?", Mathematics

magazine, v. 47, no. 4, September 1974, pp. 214-218• Bankoff, Leon, "The golden arbelos", Scripta Mathematica, v. 21, no1, March 1955,

pp.70-76• Gaba, M.G., "On a generalization of the arbelos,", the American mathematical Monthly,

v. 47, January 1940, pp.19-24

• Gardner, Martin, "Mathematical Games", Scientific American, Jan 1979, vol 240, 18-28

• Posamentier, Alfred and Gordon Sheridan, Investigations in Geometry, Addison-

Wesley, 1982

Billiards• Bender, et al, Billiard Ball Problems on Unusual Tables, COMAP• Carroll, Lewis, Circular Billiards• DeTemple, Jack and Duanene Robertson, The Calc Handbook, pp. 197-201 (billiards

on conics)• Mizerak, Steve, Inside Billiards• Olivastro, Dominic, Hall of Mirrors, Science, v. 32 no. 1, Jan-Feb 1992, pp.54-56• Pardon, George Frederick, Billiards; Its Theory and Practice• Schoenberg, Isaac J., Mathematical Time Exposures• Wells, David, Hidden Connections, Double Meanings, pp. 126 – 128

Cavalieri's Principle• Eves, Howard, Two Surprising theorems on Cavalieri Congruence, the College

Mathematics Journal, march, 1991

Chinese Geometry• Chinese mathematics : a concise history. / Li, Yen, 1892-1963. / Oxford Oxfords# 1987

QA 27 C5 L4713 1987 PCL Stacks• Swetz, Frank, The Volume of a Sphere: A Chinese Derivation, Mathematics

Teacher, February, 1995, 142 - 145

Collinearity of points and Concurrency of lines


Wesley, 1982

Congruence conditions for triangles• Beran, Davis, SSA and the Steiner-Lehmus theorem, Mathematics teacher, May 1992,

380-383

Conic Sections• Broman, Arne and Lars Broman, Museum Exhibits for the Conics, Mathematics

Magazine, vol 67, June, 1994, pp. 206 – 209• Dawson, John W. Jr., Displaying the Conics: Three alternatives to computer graphics,

Primus, vol.1, no.1, March, 1991• Downs, J. W., Practical Conic Sections, Dale Seymour, 1993• Drunker, Daniel, Reflection Properties of Curves and Surfaces, Mathematics Magazine,

June 1992• Land, Frank, The Language of Mathematics, Doubleday, 1963, pp. 147 – 159 ,206 –

214• Schupp, H, Applications and Geometry, in M. Niss et al, ed., Teaching of Mathematical

Modeling and Applications, Ellis Hoorwood, 1991, pp. 220-229 QA401 T433 PMA• F. Van Maanen, Seventeenth century instruments for drawing conic sections,

Mathematical Gazette 76:476 (1992) 222-230• Worksheet from the San Francisco Exploratorium, Sourcebook, Urban Mathematics

Collaboratives, 1990, SB-12• De Temple, Duane, A Direct Derivation of the Equations of the Conic Sections,

Mathematics Teacher, March 1990

Constructing geometric figures from string• Bolt, Brian, More Mathematical Activities for Teachers, Cambridge University Press,

1985, pp. 63-66, 70 -71, 156 - 157• Cundy, Henry M. and A.P. Rollett, Mathematical Models, 1961• Dixon, Robert, Mathographics, Dover, 1987, pp.75-78• Gardner, Martin, Penrose Tiles to Trapdoor Ciphers• Lyng, Merwyn J., Dancing Curves: A Dynamic Demonstration of Geometric

Principles, NCTM 1978• Pedoe, Dan, Geometry and the Visual Arts• Pohl, Victoria, How to Enrich Geometry using String Designs, Dale Seymour• Somervell, Edith L., A Rhythmic Approach to Mathematics, NCTM, 1975• Steinhaus, Hugo, Mathematical Snapshots• Winter, John, String Sculpture, Creative Publications• NCTM, Multisensory Aids in the Teaching of Mathematics, Eighteenth Yearbook, 1945• Seymour, Dale, Geometric Design, Dale Seymour Publications, 1988

Constructing regular polygons

• Ball and Coxeter

• Bold, Famous Problems of Geometry

• DeTemple, Duane W., Simple Constructions for the Regular Pentagon and

Heptadecagon, Math. Teacher, May 1989 (contains other refs) Mathematics Teacher,

March 1990, p. 228

• DeTemple, Duane W., Carlyle Circles and the Lemoine Simplicity of Polygon

Constructions, American Mathematical Monthly,v.98, n0. 2, February 1991, pp.97-108

• Dixon, Robert, Mathographics, Dover, 1987, pp. 34-44, 52-53

Constructing triangles


Wesley, 1982

Cross Sections of Solids• Hunt, Richard A., Calculus with Analytic Geometry• Wells, David, The Penguin Dictionary of Curious and Interesting Geometry, p. 195• Wenniger, Magnus, Dual Models

Crystals• Baeyer, Hans C., Impossible Crystals, Discover 11, February, 1990, 69 – 78• Tromba, Anthony. / Mathematics and optimal form. / New York 1985 BH 301 N3 H55

1985 PCL Stacks (Article by Wulff)

Curves of Constant Width• Caldwell, J.H., Topics in recreational mathematics, QA 95 C28 UGL• Rademacher, Hans and Otto Toeplitz, The Enjoyment of Mathematics, Dover Selected

Papers in Geometry, pp. 292-294• Smith, Scott, Drilling Square Holes, Mathematics Teacher, vol 86, no.7, October, 1993,

pp. 579 - 583 (Contains more references.)• Smart, Modern Geometries, section 3.6Cycloids, Epicycloids, and Hypocycloids• Bolt, Brian, Mathematics Meets Technology, Cambridge Univ press, 1991, pp.112-113,

118

Dimensions• Abbot, E., Flatland• Banchoff, Thomas F., Discovering the Fourth Dimension, Natick, MA: PrimComputer

Inc., 1987• Bragdon, Claude, Projective Ornament, Dover.• Burger, Dionys, Sphereland: A Fantasy About Curved Spaces and an Expanding

Universe, New York: Harper and Row 1965• Critchlow, Keith, Order in Space, New York, Thames and Hudson, 1969• Dewdney, A. K., Planiverse• Eckhart, Ludwig, Four-dimensional Space• Henderson, Linda, The Fourth Dimension and Non'Euclidean Geometry in Modern Art• Hess, Adrien L., and Carl Diekhans, The Number of Segments Needed to Extend a

Cube to N Dimensions, Mathematics Magazine 43 (September1970), 187-92• Hess, Adrien L., Viewing Diagrams in Four Dimensions, Mathematics Teacher 64

(March 1971), 247-48• Hess, Adrien L., Four-Dimensional Geometry -- An Introduction, NCTM, 1977

• Hilbert and Cohn-Vossen, Geometry and the imagination• Loeb, Space Structures: Their Harmony and Counterpoint, Birkhauser, 1976, QA 491

L63• Manning, Henry Parker, The Fourth Dimension Simply Explained, New

York,macmillan, 1911• Manning, Henry Parker, Geometry of Four Dimensions, New York, Dover, 1956• Marr, Richard, Four Dimensional Geometry, Houghton Mifflin, 1970• Miyazaki, K., An Adventure in Multidimensional Space: The Art and Geometry of

Polygons• Peterson, Ivers, The Mathematical Tourist, New York, Freeman, 1988• Rucker, Rudy, geometry, Relativity, and the Fourth Dimension• Rucker, Rudy, Miindtools, The Five Levels of Mathematical Reality, Boston, Houghton

Mifflin, 1987• Rucker, Rudy, ed., Speculations on the Fourth Dimension, Selected Writings of Charles

H. Hinton, New York, Dover, 1980• Rucker, Rudy, The Fourth Dimension, Toward a Geometry of Higher Reality, Boston,

Houghton Mifflin, 1984• Senechal, Marjorie and G. Fleck, Shaping Space: A Polyhedral Approach, Birkhauser,

1988• Steen, Lynn, A. On the Shoulders of Giants: New Approaches to Numeracy Arithmetic

Teacher, vol 37, no 6, February 1990• Weeks, Jeffrey R., The Shape of Space, Marcel Dekker, 1985, QA 612.2, W44, 1985,

PMA

Dissecting geometric figures

• Anglin, R.H. and R. Robinson Rowe, J.R. M. 8(20), 1975,149-50

• Coffin, Stewart T. The Puzzling World of Polyhedral Dissections, Oxford, U. Press,

1990

• Galvin, Fred Letter to the Editor, Amer Math Monthly, Feb 1990, p.131

• Gardner, Martin, Penrose Tiles and Trapdoor Ciphers QA 95 G 298 PMA

• Kierstead, Friend H., Jr. and R.S. Johnson, J.R.M. 9(1), 61-63, 1976 (?)

• Harry Lindgren, Recreational Problems in Geometric Dissections and How to Solve

Them . Revised and enlarged by Greg Frederickson. New York: Dover Publications,

1972.

• Frederickson, Greg N, Dissections: Plane & Fancy. New York: Cambridge University

Press, 1997.

• Wills, Herbert, III, Leonardo's Dessert: No Pi, NCTM, 1985

Dissections (2 and 3 D)

• Bolt, Brian, The Amazing Mathematical Amusement Arcade, Cambridge, 1984• Buchman, Edwin, The impossibility of Tiling a convex region with unequal equilateral

triangles, American Mathematical Monthly, Dec 1981, pp. 748-753• Caldwell, J.H., Topics in recreational Mathematics, QA 95 C28 UGL• Coffin, The Puzzling World of Polyhedral Dissections, Oxford U. Press, 1991

• Domoryad, A.P. tr. Moss, Halina, Mathematical Games and Pastimes, Macmillan, NewYork, 1964, pp. 158-65, 193-201)

• Eves, Howard, a Survey of Geometry• Fry, Erin K. and Peter L. Glidden, Illustrating Mathematical Connections: A Geometric

Proof of Euler's Theorem, Mathematics Teacher, January, 1996, pp. 62 – 65• Hunter, J. A.. H. and Madachy, Joseph S., Mathematical Diversions, Van Nostrand,

New Jersey, 1962, pp. 56-67• Langman, Harry, Play Mathematics, Hafner, New York, 1962, pp. 119-55• Langman, Harry, Geometric Dissections, D. Van Nostrand, Princeton, New Jersey, 1964• Musser, Gary L. and Burger, William F. Mathematics for Elementary Teachers,

Macmillan, New York, 1988, p.516• Soifer, Alexander, How Does One Cut a Triangle?, Center for Excellence in

Mathematical Education (885 Red Mesa Dr., Colorado Springs, CO 80906); xiii + 139pp, $18.95 (P). ISBN 0-940263-01-7

• Yates, Robert C., Geometrical Tools, Educational Publishers, 1949. 744 Y 27 (UGLI)

Duplicating the cube

• Ball and Coxeter Bold, Famous Problems of Geometry

Erroneous proofs in geometry


• Carroll, Lewis, The Lewis Carroll Picture Book

• Fetisov, A.I., Proof in Geometry, Mir

• Gardner, Martin, Wheels, Life and Other Mathematical Amusements, pp. 51-59

• D.A. Maxwell, Fallacies in Mathematics (Cambridge, 1961)

• Ya. S. Dubros (Dubnov?), Mistakes in Geometric Proofs (Heath, 1963)

• Bradis, Lapses in Mathematical Reasoning, QA 43 B6953

• Lakatos, I., Proofs and Refutations: the Logic of Mathematical Discovery

• Northrop, E.P., Riddles in Mathematics, Van Nostrand, 1944


Wesley, 1982

• Posamentier, Alfred J.H. banks, and R.L. Bannister, Geometry, Its Elements and

Structure, McGraw-Hill, 1977, pp.242-244, 270-271

Euler's formula

• Coxeter, H.S.M., Introduction to Geometry

• Mortenson, Michael, Geometric Modeling


• Pedoe, Dan, Geometry and the Visual Arts

• Barr, Stephen, Experiments in Topology, 1964, Dover

• Courant and Robbins, What is Mathematics

• Hilbert and Cohn-Vossen, Geometry and the Imagination

• Loeb, Space Structures: Their Harmony and Counterpoint, Birkhauser, 1976, QA 491

L63

• Lord, E.A.. and Wilson, C.B., The Mathematical Description of Shape and Form, 1984

• Lyusternik, L.A., Convex Figures and Polyhedron, 1963, Dover

• Newman, James, The World of Mathematics

• V.N.R. Concise Encyclopedia of Mathematics, Van Nostrand

Fibonacci Sequence• Daniel C. Litchfield and David A. Goldenheim with support from Charles H.Detrich,

Euclid, Fibonacci, Sketchpad, Mathematics Teacher, January 1997. p 8 - 12

Fivefold symmetry

• Hatigittai, Istvan, Fivefold Symmetry, 1992

Fractal geometry

• Barnsley, Michael, Fractals Everywhere

• Barcellos, Anthony, The Fractal Geometry of Mandelbrot, College Mathematics Journal

15, March 1984, 98-114

• B/W Fractals, Macintosh and Hypercard programs, $8.99 from Somak Software, 535

Encinitas Blvd, Encinitas, CA 92024, (619) 942- 2556

• Devlin, Keith, Mathematics: the New Golden Age Encyclopedia of Physical Science and

Technology, Vol 5

• Garcia, Linda, The Fractal Explorer, 1990


• Falconer, K.J., The Geometry of Fractal Sets, Cambridge, 1985

• Feder, Jens, Fractals, 1988, Plenum Press

• Kern, Jane F. and Cherry C. Mauk, Exploring Fractals - A Problem-Solving Approach

using Mathematics and Logo, Mathematics eacher, March 1990

• Lam, Lui, ed., Nonlinear Physics for Beginners, World Scientific Publishers, 199

• Long, 1981, Pascal's triangle and p self-similarity (ICM 90 ref)

• Mandlebrot, Benoit B., The Fractal Geometry of Nature

• MandelZot v2.0, Macintosh program, $8.99 from Somak Software, 535 Encinitas Blvd,

Encinitas, CA 92024, (619) 942-2556

• McDermott, Jeanne, Geometrical Forms Known as Fractals Find Sense in Chaos,

Smithsonian 14, December 1983, 110-117

• McWhorter, William, A., Jr, and Jane Morrill Tazeleer, Creating Fractals, Byte 12,

August 1987, 123-128

• Peitgen, Heinz-Otto, The Beauty of Fractals

• Peitgen, et al, Fractal Cosmos 1990 Calendar (ref Math Teacher Dec 89)

• Peterson, Ivars, "Ants in Labyrinths" and "The Dragons of Chaos", in The Mathematical

Tourist

• Schroeder, Manfred, Fractals, Chaos, Power Laws, 1992

• Six Worlds, IBM PC and compatibles 5-1/4" diskette, Turing Omnibus, Box 1456,

London, ON N6A 8M2 (Review Math Teacher, May 1989)

• Newman, Rochelle and Martha Boles, The Golden Relationship: Art, Math, Nature

• Various materials available from Media Magic, Box 507B, Nicasio, CA 94946

• Wolfe, 1984, Fractal dimension (ICM 90 ref)

• Bannon, Thomas J., Fractals and Transformations, Mathematics teacher, March, 1991,

178ff

• Barton, Ray, Chaos and Fractals, Ma thematics Teacher 83, October 1990, 524-29

• Bolt, Brian, More Mathematical Activities, Cambridge University Press 1985, pp. 72-74,

157-158

• Camp, Dane R., A Fractal Excursion, Mathematics Teacher, April, 1991, pp. 265 ff

• Devaney, Robert Chaos, Fractals and Dynamics: Computer Experiments in

Mathematics, Addison Wesley, 1990, Ch 9

• Lauwerier, Hans, Fractals: Endlessly Repeated Geometrical Figures, QA 614.86 L3813

1991 PMA

• Martin, Tami, Fracturing Our Ideas about Dimension, NCTM Student Math Notes,

insert in NCTM News Bulletin, november, 1991

• Nievergelt, Yves, Fractals on Hewlett-Packard Supercalculators, New Directions in Math

series, Wadsworth, 1991, $8

• Norton, Alec, Review of Measure, Topology, and Fractal Geometry, by Gerald A. Edgar,

American Mathematical Monthly, April 1992, p. 378 [Parts of the review will be too

technical, but other parts are relevant.]

Geodesic structures

• Edmondson, Amy C. A Fuller Explanation: The Synergetic Geometry of R.

Buckminster Fuller, Birkhauser, 1987

• Fuller, Buckminster, Utopia or Oblivion: the Prospects for Humanity

• Kenner, Hugh, Geodesic Math and How to Use It

• Laycock, Mary, Bucky for Beginners, Dale Seymour

• Mottel, Syeus, Charas: The Improbable Dome Builders

• Prenis, John, The Dome Builder's Handbook

• Wenniger, Magnus, Spherical Models

• Yarnall, William, Dome Builder's Handbook no.2

• Bolt, Brian, More Mathematical Activities for Teachers, Cambridge University Press,

1985, pp. 45 - 50 (rigid structures)

• Kenner, Hugh. / Geodesic math and how to use it. / Berkeley 1976 TH 2170 K46

Architecture Library

• Pugh, Anthony, Polyhedra, a Visual Approach, Univ.of California Press, 1976

• Domebook 2, Pacific Domes, 1971

Geometric constructions by paper folding

• Cundy, Henry M. and A.P. Rollett, Mathematical Models, 1961

• Fukuta, Jiro, Problem E 3369, Amer Math Monthly, Feb 1990, p. 150

• Johnson, Donovan, Paper folding for the Mathematics Class NCTM, 1957

• Martin, George E., Transformatio Geometry, Springer, section 5.2

• Olson, Alton T., Mathematics through Paper Folding, NCTM, 1975 (?)

• Pappas, Theoni, Mathematics Appreciation, Dale Seymour


• Row, T. Sundara, Geometric Excursions in Paper Folding

• Smart

• Yates, Robert, Carl, Geometrical Tools, QA 464 Y3 1949

Geometrical Puzzles

• Bolt, Brian, Mathematical Cavalcade• Bolt, Brian, More Mathematical Activities• Conway, J. and Guy, R., Winning Ways• Domoryad, A. P., Mathematical games and pastimes• Dunn, Angela, Mathematical Bafflers, Dover• Klarner, D., Thr Mathematical Gardener• Moscovich, Mind Benders, Games of Shape• Mott-Smith, Geoffrey, Mathematical Puzzles, Dover• Slocum, J. and Botermasn. J., Puzzles Old and New

Geometric quilt designs

• Labelle, Judith and Carol Ann Waugh, Patchworking

• Washburn and Crowe

Geometry in Animal Form and Function

• Haldane, J. B. S. (John Burdon Sanderson), 1892-1964. / On being the right size andother essays. / Oxford 1985 QH 311 H318 1985 Life Science Library

• Stewart, Ian and Martin Golubitsky, Fearful Symmetry, Penguin, 1992, chapters 7 and 8• Thompson, D'Arcy Wentworth, On Growth and Form (2 vols), Cambridge U. Press,

1972

Geometry in Ancient China

• Knorr, Wilbur, textual Studies in Ancient and Medieval Geometry, Birkhauser, 1989

Geometry in Architecture

• Baglivo, Jenny, and Jack A. Graver: Incidence and Symmetry in Design andArchitecture, Cambridge Universtiy Press, Cambridge, 1983

• Hay, D. R., The Orthographic Beauty of the Parthenon, 1853• Ghyka, Matila, The Geometry of Art and Life, Dover• Pedoe, Dan, Geometry and the Visual Arts• Mathematics Teacher, January, 1990• Salvadori, Mario, Why Buildings Stand Up, W.W. Norton, 1980

Geometry in Astronomy

• McGraw-Hill Encyclopedia of Science and Technology

• Milnor, John, On the geometry of the Kepler problem, Amer Math

Monthly 90(1983)353-364

• Rosenfeld, B.A. and M.D. Sergeeva, Stereographic Projection, Mir

• Saari, Donald g., A Visit to the Newtonian N-body Problem via Complex Variables,

Amer. Math Monthly 97, Feb 1990

Geometry in Design• Baglivo, Jenny, and Jack A. Graver: Incidence and Symmetry in Design and

Architecture, Cambridge Universtiy Press, Cambridge, 1983• Barratt, Krome, Logic and Design, the Syntax of Art, Science and Mathematics,

Eastview, Westfield, NJ, 1980• Edwards, Edward B., Pattern and Design with Dynamic Symmetry: How to Create Art

Deco Geometric Designs, Dover• Hambridge, Jay, The Elements of Dynamic Symmetry, Dover• Loeb, Arthur L., Concepts and Images: Visual Mathematics, Birkhauser, 1993, QA 36,

L64, 1993, PMA

Geometry of Crystals and Molecular Structure• American Scientist, January-February 1993 "a variety of insights that geometric

methods give into fullerenes."• Buerger, Martin Julian, Introduction to Crystal Geometry• Gallian, Joseph A., 1986, Contemorary Abstract Algebra, Heath, Chapter 30• Galiulin, R.V., Diamond Latticework: The fearful symmetry of crystalline structures,

Quantum, Jan/Feb 1991, pp. 6-11

• Gallian, Joseph A., 1986, Contemorary Abstract Algebra, Heath, Chapter 30• Hilbert and Cohn-=Vossen, Geometry and the Imagination• Holden, Alan. / Crystals and crystal growing. / 1st ed. Garden City, NY 1960, QD 921

H58 Undergraduate Library• Holden, Alan. / The nature of solids. / New York 1965 531 H711N• Klein, Herbert, Manula of Minerology• Mercer, Ian F., Crystals, Harvard University Press, Cambridge, MA, 1990 (Elementary,

good pictures)• Montesinos, Jose Maria, Classical tessellations and three-manifolds 1944- / Berlin

1987, QA 166.8 M66 1987 Phys-Math-Astron Library (the mathematics may be tooadvanced, but it has some good pictures)

• Newman, The World of Mathematics• Smith, Deane, Bibliography on molecular and crystal structure models• Steinhardt, Paul, American Scientist, v.74, 1986, p. 586 (quasicrystals)• Senechal, Marjorie, Crystalline Symmetries: An Informal Mathematical Introduction• Senechal, Marjorie and G. Fleck, Shaping Space: A Polyhedral Approach, Birkhauser,

1988• Steinhardt, Paul, Endeavor, v. 14, 1990, p. 112 (quasicrystals)• Sterling, Bruce, Buckymania, Fantasy and Science Fiction, July, 1992, 85-90• http://www.nyu.edu/pages/mathmol/K_12.html

Geometry of Escher Prints

• Coxeter, H.S. M., M. C. Escher Art and Science, North Holland, 1986• Ernst, The Magic Miirror of M.C. Escher, Random HOuse, 1984• Escher, M. C., Escher on Escher, exploring the infinite, Harry N. Abrams, 1989• Escher, M. C., Graphic Work of Escher, M. C., Hauthor Books, 1960• Escher, M. C., Universe of Mind Play• Schattschneider, Doris, Visions of Symmetry, W.H. Freeman, 1990• WORLD OF ESCHER, INC., http://www.texas.net/escher/

• Art and Man, Dec 1985/Jan 1986, "How Escher Created", pp.4-5

• Britton, Jill, and Dale Seymour, Introduction to Tessellations

• Gardner, Martin, Mathematical Carnival

• MacGillavry, Caroline, Fantasy and Symmetry: The Periodic Drawings of

M.C. Esher

• MacGillavry, Symmetry Aspects of Escher's Periodic Drawings, Scheltman and

Hokema, Bohn, 1976

• M.C. Escher: Art and Science


Geometry of Galileo• Galileo, Galilei, Operations of the Geometric and Military Compass

Geometry of Golf• Beasley, John D., The Mathematics of Games, Oxford Univ Press, 1989• Boomer, Perry, On Learrning Golf, Knopf, 1846, pp. 187-196

• Clemence, Willian James, A cinematographical study of the variation in momentumwhen swinging varying clubhead weights

• Jones, Robert Tyre, Bobby Jones on The Basic Golf Swing, Doubleday, 1969, pp.54,57, 62-3

• Thomas, Alvin, The use of a visual perceptual device in teaching the downswing in golf• Wiren, Gary, Golf, pp.16-17,26-27, 34-35, 42-45• Wrigglesworth, Frank L., A cinematographical analysis of the short chip in golf

Geometry in Higher Dimensions

• Banchoff, Thomas F., Beyond the Third Dimension, (Book 1990, video 1992)

• Francis, George K, A Topological Picture Book

• Gardner, Martin, Mathematical Carnival, MAA, 1984, QA 95 G286

• Leonardo (International Society for the Arts, Sciences, and technology), The Fourth

Dimension in Art, Science, and Mathematics, 1992

• Robbins, Fourfield: Computers, Art and the Fourth Dimension, book and video, both

1992. Software for Macintosh available for $10 from Media Magic, 1-800-882-8284

• Rucker, Rudy, The Fourth Dimension, 1984

• Steen, ed., On the Shoulders of Giants

Geometry of billiards

• Gardner, Martin, Scientific American, v. 212, May 1965

• Gardner, Martin, Scientific American, v. 236, April 1977

• Griffel, D.H., Mathematical Gazette, June, 1989

• Jepsen, Charles, Two Year College Mathematics Journal, November, 1979

• Schultz, Harris and Ray C. Shifless, Mathematical Gazette, June, 1988

Geometry of crystals

• Anderson, Hyde, Inorganic Crystal Stuuctures

• Brown and Forsyth, The Crystal Structure of Solids

• Jaffe, Howard, Introduction to Crystal Chemistry

• Lockwood, E.H., and R.H. MacMillan, Geometric Symmetr

• Wells, David, Hidden Connections, Double Meanings, Cambridge, 1988

Geometry of genetics

• Mathematics Untwists the Double Helix, Science, 23 February 1990

Geometry of Islamic art• Berggren, J.L., Episodes in the Mathematics of Medieval Islam, QA 27 A67 B46 1988

• Dury, Art of Islam• Ettinghausen and Graber, The Art and Architecture of Islam, 650-1250• Faruqui, Islam and Art• James, Islamic Art• Knorr, Wilbur, textual Studies in Ancient and Medieval Geometry, Birkhauser, 1989• Kuhnel, Islamic Arts• El-said and Parman, Geometric Concepts in Islamic Art, Dale Seymour Publications,

1976• Rice, Islamic Art• Prussin, Labelle, Hatumere: Islamic Design in West Africa• Soucek, Content and Context of Visual Arts in the Islamic World• Van der Waerden, Geometry and Algebra in Ancient Civilizations, Springer, 1983• Washburn and Crowe

Geometry of knots

• Bain, G. Celtic Art, Dover, 1973

• Brown, Ronnie, and John Robinson, Symbolism: Sculptures and Tapestries by John

Robinson, Mathematics and Knots, (School of Mathematics, U. of Wales, Bangor,

Gwynedd LL57 1UT, Wales, UK), 1989, 36 pp., £6 + £1 surface, £250 air) ISBN 0-

9514947-08. Also, 27 pp, ISBN 0-9514947-16

• Cipra, Bary A., "To Have and Have Not: When Are Knots Alike?", Science, v.242, Sept

9, 1988

• Devlin, Keith, Mathematics: the New Golden Age

• Geometry Center, Ujniversity of Minnesota, Not Knot (video), 1991

• Holden, Orderly Tangles, QA 491 H626 UGLI

• Moran, Siegfried, The Mathematical Theory of Knots, Elsevier, 1989

• Peterson, Ivars, The Mathematical Tourist

• Peterson, Ivars, "Unknotting a Knotty Tale, Science News, v. 133, May 21, 1988 "Tying

up a Knotty Loose End," Science News, v.134, Oct 29, 1988 Geometry of Molecular

Structure

• Gillespie, R.J., Molecular Geometry, Van Nostrand, 1972

• Hout, R.F. Jr., A Pictorial Approach to Molecular Structure and Reactivity, WIley, 1984

• Richards, W.G., Structure and Spectra of molecules, Wiley, 1985, pp.27-43

• Quasicrystals: Rules of the Game, Science, 2 March 1990

Geometry of optics

• Bowden and Schiffer, The role of Mathematics in Science, Chapter 3 (MAA?) (Not in

UTCat?)Consortium, November, 1986

• Herzberger, Modern Geometrical Optics, pp. 71-148, 383-420

• Leathem, The Elementary Theory of the Symmetrical Optical Instrument, pp.1-25, 39-

42, 44-57

• Martin, Geometrical Optics, pp.1-43,107-130,173-196

• Pitchford, Studies in Geometrical Optics, pp.1-12, 50-60, 72-86, 180-209

• Southall, The principles and methods of Geometrical Optics, pp.1-32, 35, 198-262


The geometry of perspective drawing

• Beskin, N.M., Images of Geometric Solids, Mir

• Leonardo (International Society for the Arts, Sciences, and technology), Art and

Technology, 1992

• Moore, Charles G., To View an Ellipse in Perspective, College Mathematics Journal,

1989, 134 – 136

• Penna, Michael A. and Richard Patterson, Projective Geometry and its Application to

Comuter Graphics

The geometry of relativity

• Penrose, Roger, The Geometry of the Universe, in Steen, Lynn A., Mathematics Today,

QA7 M3447 PMA

Geometry of textiles

• New York Times Educational Supplement, April 3, 1988 Washburn and Crowe

• Grunbaum, B., Periodic ornamentation of the fabric plane: lessons from Peruvian

fabrics, Symmetry 1(1990), 45 -68.

• Grunbaum, Branko, and G.C. Shepard, Satins and Twills: An Introduction to the

Geometry of Fabrics, Mathematics Magazine, 53, 1980, 131-161 and 313

Geometry of the kaleidoscope

• Arithmetic Teacher, February, 1970


• Brewster, Sir David, article on images in mirrors, EncyclopediaBritannica, c. 1818

(Brewster invented the kaleidoscope)

• Coxeter, Regular Polytopes

• Baker, Cozy, Through the Kaleidoscope ... and Beyond, Beechcliff Books, Annapolis,

1987 pp. 13-22,170-178, 188-195

• Mathieu, Jean Paul, Optics, parts 1 and 2, vol. 62, 1075

• Weiting, Thomas W., The Mathematical Theory of Chromatic Plane Ornaments, Marcel

Dekker, NY, 1982, pp 31-36,346-362

• Williamson, Samuel J. and Cummins, Herman Z. Light and Color in Nature and Art,

Wiley, NY, 1983, pp.223-270

The Golden Ratio in geometry

• Baravelle, H.V., The Geometry of the Pentagon and the Golden Section, Math. Teacher,

Jan. 1948

• Dantzig, Tobias, The Bequest of the Greeks

• Ghyka, Matila, The Geometry of Art and Life, Dover

• Huntley, H.E. The Divine Proportion, Dover

• Musser, Gary and William F. Burger, Mathematics for Elementary Teachers


• Ogilvy, Charles, Excursions in Geometry




Wesley, 1982

• Runion, Garth E. The Golden Section and Related Curiosa, Scott Foresman, 1972


• Vajda, S., Fibonacci and Lucas Numbers, and the Golden Section:Theory and

Applications, QA 241, V24, 1989 PMA

Indian Geometry

• Amma, T.A. Saraavati, Geometry in Ancient and Medieval India, PMA QA 444 S26

1979

• Knorr, Wilbur, textual Studies in Ancient and Medieval Geometry, Birkhauser, 1989

• Sarasvati, Svami Satya Prakesh, PMA QA 443.5 P72 1987

• Van der Waerden, Geometry and Algebra in Ancient Civilizations, Springer, 1983

• Baeyer, Hans C., Impossible Crystals, Discover 11, February, 1990, 69 – 78

• Boles, Martha and Rochelle Newman, Universal Patterns Book 1: The Golden

Relationship: Art, MAth and Nature

• Cook, Theodore A., The Curves of Life, Dover

• Hargittai, I and C.A. Pickover, Spiral Symmetry, World Scientific, 1992

• Kessler, James E., Goldern Triangle, Mathematics Teacher, April, 1994, p. 324

• Loeb, Arthur L., Concepts and Images: Visual Mathematics, Birkhauser, 1993, QA 36,

L64, 1993, PMA

• Markowski, George, Misconceptions about the Golden ratio, College Mathematics

Journal, January, 1992, 2 – 19

• Mathematics Teacher, February 1991, 133-138, The artist's View of Points and Lines

• National Council of Teachers of Mathematics, Historical Topics for the Mathematics

Classroom

• Willard, Claude-Jacques, Le nombre d'or: utilisation en mathematiques et dans les

beaux-arts, Paris, 1987

Honeycombs• Peressini, Anthony L., The Design of Honeycombs, Umap Module Unit 502• Thompson, D'Arcy, On Growth and Form, Cambridge U Press, 1917• Toth, L. Fejes, What the bees know and what they do not know, Bull. Amer. Math. Soc.

vol 70 (1964), pp. 468 - 481

Indian Geometry

• Datta, Bibhutibhusan, The Science of the Sulba, 1932• Taylor, Charles, Ancient and Modern geometry of Conics, pp. xvii-xxxiii

Inversion

• Pedoe, Dan, Acourse of Geometry, QA 445 P43 PMA

• Rosenfeld, B.A. and M.D. Sergeeva, Stereographic Projection, Mir


Japanese Geometry• Fukagawa, Hedetosi and Dan Pedoe, Japanese Temple Geometry Problems, The

Charles Babbage Research Centre, P.O. Box 272, St. Norbert Postal Station, Winnipeg,Canade, R3V 1L6, 1989

• Sokolowsky, Dan, Review of "Japanese Temple Problems", American MathematicalMonthly, April, 1991

Knots• Adams, Colin, The Knot Book: An Elementary Introduction to the Mathematical Theory

of Knots, 1994, Freeman• Gialamas. Stafanos and Gialamos, Panagiotis, Knots Everywhere, Consortium, Spring,

1993, pp. 4 - 5 (Contains other references)• Gialamas, S. Knots Everywhere, Chicago: Aristotle Press, 1993• Livingston, Charles, KNot Theory, MAA 1993 (Fairly advanced?)• Prasolov, V.V., Intuitive Topology, AMS, 1994

Line of Sight Problems• Stewart, Ian, MAthematical Recreations: Shedding litle Darkness, Scientific American

272:2 (August 1996) 100-103• Scientific American 270:5 (May 1994) 118 - 120 (Number of guards needed for an art

gallery)-

Linkages and geometry• Bolt, Brian, More Mathematical Activities for Teachers, Cambridge University Press,

1985, pp.12-14, 114• Bolt, Brian, Mathematics Meets Technology, Cambridge Univ press, 1991• Choate, Jonathan, Linkages, Consortium, Summer 1995, pp. 6 – 7• Cundy, Henry M. and A.P. Rollett, Mathematical Models, 1961• Kempe, A. B., How to draw a straight line: a lecture on linkages, Macmillan• Shyers, Joan, COMAP Module 594• Solovyov, Yury, Making the Crooked Straight: Inversors and Watt's Steam Engine,

Quantum, November/December 1990, pp. 20 – 23• Kempe, A.B., How to Draw a Straight Line, NCTM, 1977• Smart, Modern Geometry• Meserve, Bruce E., Linkages as visual aids, Mathematics Teacher 39m 1946, 372-79• Multi-sensory Aids in the Teaching of Mathematics, NCTM Eighteenth Yearbook (?• Yates, Robert, Carl, Geometrical Tools, QA 464 Y3 1949• Yates, A Mathematical Sketch and Model Book, Educat.Pub, 1949 (?)

Map coloring• K. Appel, and W. Haken, The four color proof suffices, Mathematical

Intelligencer,8(1986), 10-20• K. Appel, and W. Haken, th esolution of the four color problem, Scientific American,

October 1977, pp.108 – 121• Barnette, David, Map Coloring, Polyhedra, and the Four-Color Problem, MAA, 1984• Keeports, David, A Map-coloring algorithm, Mathematics teacher, December, 1991, pp.

759-76• Appel, Kenneth and Wolfgang Haken, The Four Color Problem, in Steen, Lynn A.,

Mathematics Today, QA7 M3447 PMA• Ball and Coxeter• Brink, Raymond W., ed, Selected Papers on Geometry QA 446 S44, PMA• Coxeter, H.M.S., The Four Color Problem, 1890-1940, Math. Teacher, April, 1959• Devlin, Keith, Mathematics: the New Golden Age• Gardiner, A., Mathematical Puzzling• Hilbert and Cohn-Vossen, Geometry and the Imagination• Ringel G., Map Color Problem• Saaty, Thomas, The Four Color Problem• Smart, Modern Geometry• Spitznagel, Edward, Selected Topics in Mathematics

Map Projections

• Consortium, Summer, 1989 (References therein)

Mayan Geometry

• Scientific American, August 1989

Minimal Surfaces

• Boys, Charles, Soap Bubbles, Dover, 1959

• Hildebrandt, Stefan and Anthony J. Tromba, Mathematics and Optimal Form, 1985

(Available from Dale Seymour)


Technology, 1992

• Taylor, Jean E., Crystals, in Equilibrium and Otherwise, video, 1990 American

Mathematical Monthly, April 1992, p. 376

• Courant and Robbins, What is Mathematics?

• Hildebrandt, Stefan and Anthony J. Tromba, Mathematics and Optimal Form

• senberg, Cyril, The science of soap films and soap bubbles, Dover

• NCTM News Bulletin, November, 1995, p. 2 ("Double Bubbles Give Mathematicians

No Trouble")

• Scientific American, 1976

• Selected Papers in Geometry, pp. 40-47

Optics

• Conrady, A. E., Applied Optics and Optical Design, vol.1, Dover• Drucker, Daniel, Reflection Properties of Curves and Surfaces, Mathematics Magazine,

June 1992• House, Peggy, Interactions of Science and Mathematics: A Set of Activities, Eric

Clearinghouse for Science, Mathematics and Environmental Education, Ohio StateUniversity, College of Education, 1200 Chambers Road, Columbus, Ohio 43212

• Maesumi, Mohsen, Parabolic Mirrors, Elliptic and Hyperbolic Lenses, AmericanMathematical Monthly, June-July 1992, pp. 558-560

• Riddle, Analytic Geometry, 3rd edition, pp. 138-143 (reflection properties of conics)

Paper Folding• Envelopes. / Boltianskii, V. G. (Vladimir Grigor'evich) / New York 1964 QA 621 B65

Physics-Math-Astronomy Library• "Excursions in Geometry" by C. Stanley Ogilvy• Dutch, Stephen, Folding n-pointed stars and snowflakes, Mathematics Teacher,

November, 1994, pp. 630 - 637

Perspective Drawing• Dixon, Robert, Mathographics, Dover, 1987, pp.79-86• Edgerton, S. Y., Jr., The Renaissance Rediscovery of Linear Perspective, Basic Books,

NY, 1975

Pick's Theorem(Overlap's with Euler's Theorem?)• Grunbaum, Branko and G. C Shephard, Pick's Theorem, American Mathematical

Monthly, February, 1993, pp 150 - 161 (Additionlal references p. 150)

Polyhedra


• Bassetti, Fred, at al, Math Projects: Polyhedral Shapes, 1968

• Critchlow, Keith, Order in Space, Dale Seymour

• Cundy, H. Martyn and A.P. Rollett, Mathematical Models, Clarendon Press, 1954

• Federico, Descartes on Polyhedra


• Hilbert and Cohn-Vossen, Geometry and the Imagination, pp.89-93, 290-295, 143-157

• Hilton, Peter, and Jean Pedersen, Build Your Own Polyhedra

• Holden, Allan, Shapes, Spaces, and Symmetry, 1971

• Jimenez,et al, The construction of Platonic bodies from constant width continuous

strips, Int J. Math. Educ. Sci. Technol, 1990, vol 21, no.1, 37-50

• Laycock, Mary, Straw Polyhedra, Creative Publications, 1970

• Lockwood, E.H., and R.H. MacMillan, Geometric Symmetry

• Loeb, et al, On the Icosahedron, the Pentagonal Dodecahedron, and the Rhombic

Triacontahedron, Symmetry, v.1, no.1, 1990, 29-36.

• Lyusternik, Convex Figures and Polyhedra\

• Ogilvy, Excursions in Geometry, pp. 129-134

• Pearce, Peter, and Susan Pearce, Polyhedra Primer, Dale Seymour



Wesley, 1982

• Senechal, Marjorie and George Fleck, Shaping Space, Birkhauser, 1988

• Toth, L. Fejes, Regular Figures, Pergamon Press, 1964

• Wenninger, Magnus J., Polydron Models, Cambridge U. Press,1970

• Wenninger, Magnus J., Polyhedron Models for the Classroom, NCTM, 1966

• Williams, Robert, The Geometrical Foundation of Natural Structure, Dale Seymour

Polyominoes


• Dudeney, Canturbury Puzzles and Others, p.119-120

• Gardner, Scientific American v. CCXIII, p.96-104

• Canadian Journal of Mathematics, vol. XXV, pp585-602

Projective Geometry

• Brill and Steuben, Demystifying the Projective Plane, Math. Magazine 63,

no.1, Feb 1990


Wesley, 1982



Proofs of the Pythagorean theorem

• Fredrichs, Kurt Otto, From Pythagoras to Einstein, QA 460 P99 F7 PMA

• Beamer, James E, Using puzzles to teach the Pythagorean Theorem, Mathematics

Teacher, May 1989

• Euclid, Elements

• Heath, Thomas, Manual of Greek Mathematics

• Loomis, Elisha Scott, The Pythagorean Proposition

• Newman, The World of Mathematics (Vol 1)


Wesley, 1982

• Prentice-Hall Encyclopedia of Mathematics, 1982

• Swetz, Frank J. and T.I. Kao, Was Pythagoras Chinese?, NCTM 1977

Proofs without words

• Various journals (Amer Math Monthly, Math Magazine)

Space Tessellations


• Critchlow, Keith, Order in Space, Dale Seymour


• Loeb, et al, On the Icosahedron, the Pentagonal Dodecahedron, and the Rhombic

Triacontahedron, Symmetry, v.1, no.1, 1990, 29-36.

• Holden, Allan, Shapes, Space, and Symmetry, 1971

• Williams, Robert, The Geometrical Foundation of Natural Structure, Dale Seymour

Quilts• Nephew, Sara, Equilateral triangle patchwork quilts, Dover• Whitman, Nancy, Line and Rotational Symmetry, Mathematics Teacher, April, 1991• Zaslavsky, Claudia, "Symmetry in American Art", Arithmetic teacher, September, 1990

Sphere Packing

• Packing your n-Dimensional Marbles, Science, 2 March 1990

• The nth Dimension, Forbes, v.138, Dec 29, 1986

• Curves for a tighter fit, Science News, v. 138, May 19, 1990, pp316-317

• Loosely packed spheres, Science News, v. 137, June 16, 1990, p. 382

• Thompson, Thomas M., From Error-correcting Codes through Sphere Packings toSimple Groups, MAA, 1984

Williams, Robert, The Geometrical Foundations of Natural Structure

Spirals

• Davis, Philip J., Spirals: From Theodorus to Chaos, 1993

• Lawlor, Robert, Sacred Geometry, 1982


Technology, 1992

• Pickover, Clifford and I. Hargittai, Spiral Symmetry, 1992

• Edwards, Edward B., Pattern and Design with Dynamic Symmetry, Dover, 1967, pp.13-

24, 45-46, 68 - 69, 92-95, 104-105, 111-112, 118-122

• Hargittai, Istvan, and Clifford A. Pickover, eds, Spiral Symmetry, QA 483 S68 1992

• Wells, David, Hidden Connections, DOuble Meanings, Cambridge, pp. 83 - 86

Squaring the circle


• Bold, Famous Problems of Geometry

• Dixon, Robert, Mathographics, Dover, 1987, pp.44

String designs• Envelopes. / Boltianskii, V. G. (Vladimir Grigor'evich) / New York 1964 QA 621 B65

Physics-Math-Astronomy Library• Irvine, Max, Cable Structures, Dover

Symmetry in physics• Altmann, Simon L., Icons and Symmetries, Oxford Univ. Press, 1992• Stewart, Ian and Martin Golubitsky, Fearful Symmetry, Penguin, 1992

Strip (frieze) patterns

• Crowe, Donald, Symmetry, Rigid Motions, and Patterns, Himap (bib)

• Hargittai, Istavan, ed., Symmetry: Unifying Human Understanding




Symmetry in Everyday Objects

• Gallian, Joseph A., Symmetry in Logos and Hubcaps

Taxicab geometry

• Krause, Eugene F., Taxicab Geometry, Addison-Wesley

• Posamentier, Alfred and Gordon Sheridan, Investigations in Geometry, Addison

Wesley, 1982

Tilings (Tessellations of the plane)


• Boorman, Phil, More About Tessellating Hexagons, Math Teacher, Summer, 1971

• Clemens, Stanley, Tessellations of Pentagons, Math Teaching, June, 74

• Coxeter, H.M.S., Twelve Geometric Essays, pp.76,115,168

• Dubrovm, Fomenko, and Novikov, Modern Geometry - Methods and Applications,

p.169

• Dunn, James, A. More About Tessellating Hexagons, Mathematics Teaching, Summer,

1971



• Grunbaum, Branko and G.C. Shepard, Tilings and Patterns, 1987

• Hilbert and Cohn-Vossen, Geometry and the Imagination

• Klarner, D.A. (ed.), The Mathematical Gardner

• Lockwood, E.H., and R.H. MacMillan, Geometric Symmetry Mathematics Teacher,

April,1974

• Mold, Josephine, Tessellations, Cambridge U. Press

• Nikulin, V.V., Geometries and Groups Scientific American, July, 1975

• Serra, Michael, Discovering Geometry, Key Curriculum Press, 1989


• Baeyer, Hans C., Impossible Crystals, Discover 11, February, 1990, 69 – 78

• Fulton, Chandler, Tessellations, American Mathematical Monthly, vol. 99, May 1992,

pp. 442 - 445.

• Classical tessellations and three-manifolds. / Montesinos, Jose Maria, 1944- / Berlin

1987, QA 166.8 M66 1987 Phys-Math-Astron Library (the mathematics may be too

advanced, but it has some good pictures

• Spatial tessellations : concepts and applications of Voronoi diagrams. / Okabe,

Atsuyuki, 1945- / Chichester, En# 1992 QA 278.2 O36 1992 Physics-Math-

Astronomy Library (See also review by Marjorie Senechal, College MAth Journal, v 26,

January 1995

• Orton, A. and S.Flors(?), Analysis of an ancient Tessellation, Mathematical Gazette, vol.

73, 1989, pp 297 - 301

Tessellatons of Space• Baeyer, Hans C., Impossible Crystals, Discover 11, February, 1990, 69 – 78• Ellott, H.A., Maclean, and Jordan, Geometry in the Classroom, Holt, Rinehart and

Winston of Canada, 1968• Gray, Jeremy, Parsimonious Polyhedra, Nature, 367 (10 February 1994) 513 – 514• Loeb, Space Structures: Their Harmony and Counterpoint, Birkhauser, 1976, QA 491

L63• Classical tessellations and three-manifolds. / Montesinos, Jose Maria, 1944- / Berli

1987, QA 166.8 M66 1987 Phys-Math-Astron Libraryn (the mathematics may be tooadvanced, but it has some good pictures)

• Orton, A. and S.M. Flower, Mathematical Gazette, v. 73, 1989, pp. 297-301• Wheeler, Dan and David Sklar, Two Year Colloege MAthematics Journal, September,

1981, p. 246

Topological surfaces

• Arnold, B.H., Intuitive Concepts in Elementary Topology

• Barr, Stephen, Experiments in Topology, 1964

• Brill and Steuben, Demystifying the Projective Plane, Math Mag 63, no1, Feb.1990

pp.48-51

• Courant and Robins, What is Mathematics, p.235-264

• Francis, George K., A Topological Picture Book

• Guillen, Michael, Bridges to Infinity,1983, pp. 153-174

• Johnson, Donovan, Topology, the Rubber Sheet Geometry, 1960

• Liepzen, W., Visual Topology, 1969

• Khurgin, Ya. Did You Say Mathematics?, Mir

• Bergamini, David, Mathematics, Life Science Library, Time-Life, 1973



• Weeks, Jeffrey, The Shape of Space, Dekker, 1985

• Pappas, Theoni, The Joy of Mathematics

• Prasolov, V.V., Intuitive Topology, AMS, 1994

Trisecting the Angle• Courant and Robbins, What is Mathematics, pp.137-138• Gardner, Martin, Mathematical Carnival, Chapter 19 (and bibliography)• Yates, Robert C., Geometrical Tools, Educational Publishers, 1949. 744 Y 27 (UGLI)• Ball and Coxeter• Bold, Famous Problems of Geometry• Dudley, Underwood, A Budget of Trisections, Speinger, 1987• Miller, Leslie, College Geometry, p. 48, 194-197, 1957• Ogilvy, Excursions in Geometry, ch 10, 1969• Posamentier, Alfred and Gordon Sheridan, Investigations in Geometry, Addison-

Wesley, 1982• Yates, Robert C., The Trisection Problem, NCTM, 1971

Topology of highway intersections

• Grazis, D., ed., Traffic Science, Wiley, 1974Consortium, Winter, 198

Wallpaper patterns

• Audsley, W. D. , Designs and Patterns from Historical Ornament, Dover

• Crowe, Donald, Symmetry, Rigid Motions, and Patterns, Himap (bib)


• Lynn, Catherine, Wallpaper in America: fron the 17th century to World War I

• Stevens, Peter, Handbook of Regular Patterns: an Introduction to Symmetry in Two

Dimensions


• Waterman, V. Ann, Design Your Own Repeat Patterns, Dover


• Christie, Archibald, Pattern Design, Dover

• Dye, Daniel Shets, Chinese Lattice Designs, Dover

• Gallian, Joseph, Contemporary Abstract Algebra, Heath, Chapter 30

• Grunbaum, Branko and G.C. Shepard, Tilings and Patterns, 1986, Freeman

• Huinker, DeAnn M. and Eugene M. Krause, Investigations in Mathematics for

Elementary Teachers, Heath, 1991, pp. 271-274

• Schattschneider, Doris, The Plane Symmetry Groups: Their Recognition and Notation,

American Mathematical Monthly 85(6) 439-450

• Stevens, Peter, Handbook of Regular Patterns, MIT Press, 2980

• Waterman, V. Ann, Design your Own Repeat Patterns, Dover

• http://www.geom.umn.edu:80/~math5337/Wallpaper/

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M333L - BIBLIOGRAPHY FOR TOPICS – SPRING 2003 · M333L - BIBLIOGRAPHY FOR TOPICS – SPRING 2003 Abstract symmetry in mathematics and physics • Bunch, Bryan, Reality's Mirror